AnswersSSCR 26 Math Essentials ARational Numbers

Rational Numbers Answers

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1
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Which of the following could represent a diver’s position in relation to the surface of the water after diving into a pool? Select all that apply.

A
3 meters
B
-2 meters
C
-3.1 meters
D
meters
Option D
E
meters
Option E
2
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0.26

A
0.26
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

Marco states that 7.696696669…… is a rational number because it is a repeating decimal. Is he correct? Justify your answer.

Answer:

Marco is not correct. Although the decimal has a pattern, it is not a repeating decimal because the same sequence of digits does not repeat infinitely. In this number, the number of 6s increases each time (69, 669, 6669), which means the decimal does not terminate and does not repeat a fixed cycle. Therefore, it is an irrational number, not a rational number.

4

Sample Response: No, Marco is not correct. The number does not actually repeat because after each 9 there is an additional 6 before the next 9. The number is not a rational number. Select all the information you included in your response.Marco is not correct.69, and 669, and 6,669 are not the same.A repeating decimal must have a digit or a group of digits that repeat.This is not a rational number.

A
Marco is not correct.
B
69, and 669, and 6,669 are not the same.
C
A repeating decimal must have a digit or a group of digits that repeat.
D
This is not a rational number.
5

A diver swims 5.875 feet up to the surface of the water. Which number represents the diver’s position in relation to the surface before swimming to the top?

A
-5.9 feet
Option A
B
feet
Option B
C
-58 feet
Option C
D
feet
Option D
6

What is the equivalent decimal value for this scale?

A
0.008
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

ABCD

A
A
B
B
C
C
D
D
8

Which rational number is the additive inverse of -0.75?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

Which of the following are true statements? Select all that apply.

A
All integers are rational numbers.
B
Repeating decimals are not rational numbers.
C
is not a rational number.
Option C
D
Terminating decimals are rational numbers.
E
0.278254 is a terminating decimal, therefore it is a rational number.
10

Which pairs of rational numbers are equivalent? Select all that apply.

A
-0.5 and
Option A
B
and
Option B
C
and 0.55
Option C
D
and -0.02
Option D
E
0.15 and
Option E
11

In the last ten games, Jamal made 79 of his free throws and Brian made 58 of his free throws. Which player has the better record? Explain.

Answer:

Jamal has the better record. To compare his 7/9 to Brian's 5/8, convert both to decimals. Jamal's record is 0.7 repeating (0.777...), and Brian's record is 0.625. Since 0.777... is greater than 0.625, Jamal made a higher percentage of his free throws.

12

Sample Response: Jamal has the better record because his record is 0.7 and Brian’s record is 0.625. Jamal made more free throws. Select all the information you included in your response.Jamal has the better record.Jamal made of his free throws.Brian made 0.625 of his free throws.Comparing the tenths digit of each decimal shows that Jamal has the greater value.

A
Jamal has the better record.
B
Jamal made of his free throws.
C
Brian made 0.625 of his free throws.
D
Comparing the tenths digit of each decimal shows that Jamal has the greater value.

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